A Biologist's Guide to Mathematical Modeling in Ecology and EvolutionThirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own.
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Contents
1 | |
17 | |
Deriving Classic Models in Ecology and Evolutionary Biology | 54 |
Functions and Approximations | 89 |
Numerical and Graphical TechniquesDeveloping a Feeling for Your Model | 110 |
Equilibria and Stability AnalysesOneVariable Models | 151 |
General Solutions and TransformationsOneVariable Models | 191 |
Linear Algebra | 214 |
Probability Theory | 513 |
Probabilistic Models | 567 |
Analyzing Discrete Stochastic Models | 608 |
Analyzing Continuous Stochastic ModelsDiffusion in Time and Space | 649 |
The Art of Mathematical Modeling in Biology | 692 |
Commonly Used Mathematical Rules | 695 |
Some Important Rules from Calculus | 699 |
The PerronFrobenius Theorem | 709 |
Equilibria and Stability AnalysesLinear Models with Multiple Variables | 254 |
Equilibria and Stability AnalysesNonlinear Models with Multiple Variables | 294 |
General Solutions and TransformationsModels with Multiple Variables | 347 |
Dynamics of ClassStructured Populations | 386 |
Techniques for Analyzing Models with Periodic Behavior | 423 |
Evolutionary Invasion Analysis | 454 |
Finding Maxima and Minima of Functions | 713 |
MomentGenerating Functions | 717 |
725 | |
727 | |